Homework Set # 8, due April 14, 2008
1. Consider the integral
I=
0
g(x)dx log(1 + ex )
(1)
with g(x) the level density that is slowly varying at the Fermi level. a) Derive the low temperature expansion of this integral to order 1/. b) Find numerically the
Homework Set # 6, due April 1, 2009
1. Show that the binding energy of a weakly bound state such as the deuteron can be
related to the scattering length by
2
Ebinding =
2ma2
.
(1)
2. Consider matrix elements of the quadrupole moment operator
J M |Q33 |JM
Homework Set # 5, due March 23, 2009
1. Consider the classical eld theory
1
L=
2
2
3
( a )2 ,
= 13 2 = 1.
a
with
=1 a=1
(1)
a
a) Given that s (S2 ) = Z argue that this theory has topological solutions of nite
energy.
Show that
Q=
1
8
2
abc a b c d x
(2)
Homework Set # 2, due February 16, 2009
1. Show that the Higgs mechanism does not give mass to the photon.
2. Show that the part of the weak Lagrangian describing the interactions of quarks and
the Z-boson is given by
L0 =
g
2 cos W
q (gV gA 5 )q Z .
q
F
Homework Set # 3, due March 2, 2009
1. Show that K0 and K+ satisfy the relation Q = 1 Y + I3 .
2
2. Let Tij be a tensor that transforms as
Ti j = Ui i Uj j Tij ,
(1)
with U U (N ).
a) Show that (Tij + Tji )/2 and (Tij Tji )/2, retain their symmetry after
Homework Set # 9, due May 4, 2009
1. The nuclear Hamiltonian is given by
H = Hstrong + Heletromagnetic + Hweak
(1)
The aim of this problem is to show that CP violation of the nuclear Hamiltonian can
in principle be observed from the distribution of the sp
Homework Set # 9, due April 21, 2008
1. Consider the spectrum of a square box given by Enm = n2 + with m and n positive integers. a) Unfold the spectrum and make a histogram of the rst 1000 spacings. Compare with the Poisson distribution. b) Do the same f
Homework Set # 10, due April 28, 2008, Last Set
1. Calculate the 3 (L) statistic for the two-point correlator sin2 r 2 r2 to leading order in L for large L. 2. Show that (Ek El ) = detAkl
k>l
(1)
(2)
with Akl = Elk1 . First show that this identity is corr
Homework Set # 2, due February 18, 2007
1. Show that the Higgs mechanism does not give mass to the photon. 2. Show that the part of the weak Lagrangian describing the interactions of quarks and the Z-boson is given by L0 = g 2 cos W q (gV GA 5 )q Z .
q
(1
Homework Set # 3, due March 10, 2008
1. Show that K0 and K+ satisfy the relation Q = 1 Y + I3 . 2 2. Let Tij be a tensor that transforms as Ti j = Ui i Uj j Tij , with U U (N ). a) Show that (Tij + Tji )/2 and (Tij Tji )/2, retain their symmetry after tra
Homework Set # 1, due February 11, 2007
1. Derive the formula for Mott cross section (see R. Hofstadter, Ann. Rev. Nucl. Sci. 7, 231 (1958).
a a a 2. Shown that F F is gauge invariant with F give by a F = Aa Aa + gCabc Ab Ac ,
(1)
and Cabc the structure
Homework Set # 5, due March 24, 2008
1. Consider the classical eld theory 1 L= 2
2 3
( a )2 ,
=1 a=1
with
a
= 13 2 = 1. a
(1)
a) Given that s (S2 ) = Z argue that this theory has topological solutions of nite energy. Show that Q= 1 8
2 abc a b c d x
(2)
i
Homework Set # 7, due April 6, 2008
1. Experimental nuclear physicists have been looking for superheavy nuclei. Propose three dierent sets of Z and N that are particularly promising and argue why they are promising. 2. Give a derivation of the electric di
Homework Set # 5, due March 31, 2008
1. Show that the binding energy of a weakly bound state such as the deuteron can be related to the scattering length by
2
Ebinding =
2ma2
.
(1)
2. Consider matrix elements of the quadrupole moment operator J M |Q33 |JM